Research On Some Problems Of Locality Preserving Projections

With the rapid development of information age, the real world produces moreand more data, especially for the high dimensional data, which brings with theunprecedented dimension disaster while enriching and improving everyone’s life.Howto deal with the high dimensional data becomes a more attentive problem.Therefore,the dimension reduction of data becomes the focus of attention in contemporary.The data dimension reduction methods at present,mainly have two kinds,the firstis the linear dimension reduction method,which maps the sample data,that is highdimensional data,into low dimensional space.But in the real world,data are almostdistributed in a nonlinear manifold,and the traditional linear dimension reductionmethod is unable to learn nonlinear geometric structure of data.Therefore,the scholarshave put forward the second kind of data dimension reduction method, nonlineardimension reduction method,which is so-called manifold learning method,finding outthe local linear features of the sample data,and mapping nonlinearly to a global lowdimension space.Despite manifold learning method could effectively learn the essentialcharacteristics of a nonlinear manifold,they abandoned some advantages of lineardimension reduction method.For example,if a new data will add,manifold learningmethod need to recalculate all data to obtain low dimensional feature of the new datapoint,which made the efficiency of computation too low.Aim at this problem,HeXiaofei and others put forward Locality Preserving Projections algorithm basing onLaplacian Eigenmaps method.However,LPP,as a unsupervised learning method, hasnonefficient use of the known classification information of training points,and globaluse of the same neighborhood parameter so as to the inefficient classification.This paper specializes in studying and improving Locality PreservingProjections method for the two problems.The main work as following:(1) This paper gives Supervised Locality Preserving Projections based on classinformation algorithm for the research of supervised method of Locality Preserving Projections,which applies the supervised method based on class information totraditional unsupervised Locality Preserving Projections algorithm;(2) This paper gives Locality Preserving Projections based on improvement ofneighborhood algorithm for the research of the effect of neighborhood factor onLocality Preserving Projections method, which defines a new distance matrix to buildneighborhood graph in order to get efficiently the essential information of highdimensional data in low dimensional space.Meanwhile, this paper gives a large number of numerical experiments to illustratethe improved algorithms can improve the recognition rate of the high dimension data,and have practical significance on face recognition and other fields.